File:Archimedean Spiral animation with Gears in and out tracing.gif
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Archimedean_Spiral_animation_with_Gears_in_and_out_tracing.gif (433 × 331 pixels, file size: 4.26 MB, MIME type: image/gif, looped, 355 frames, 17 s)
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DescriptionArchimedean Spiral animation with Gears in and out tracing.gif |
English: Archimedean Spiral animation with Gears in and out tracing |
Date | |
Source | Own work |
Author | Jahobr |
Other versions |
|
GIF development InfoField | |
Source code InfoField | MATLAB codefunction [] = Archimedean_Spiral_animation_with_Gears()
% Source code for drawing gears that produces archimedean spiral.
% The shape of the gears is not precise, it creates a decent GIF and a SVG.
%
% 2019-02-17 Jahobr
RGB.bkgd = [1 1 1 ]; % white background
RGB.black = [0 0 0 ]; %
RGB.red = [1 0.2 0.2]; %
RGB.blue = [0.2 0.2 1 ]; %
RGB.brightGrey = [0.8 0.8 0.8]; % gear
RGB.grey = [0.5 0.5 0.5]; % rack
RGB.darkGrey = [0.3 0.3 0.3]; % marks
RGB.green = [0.1 0.7 0.1]; %
RGB.violet = [0.6 0.2 0.8]; %
RGB.cyan = [0 0.8 0.8]; %
RGB = structfun(@(q)round(q*255)/255, RGB, 'UniformOutput',false); % round to values that are nicely uint8 compatible
[pathstr,fname] = fileparts(which(mfilename)); % save files under the same name and at file location
teeth = 16; % use "highly composite number"
module = 1/8; % gear size
for versionNr = 1:3
if versionNr == 1
curVers = 'positive_tracing';
nFrames = 355;
accFrames = 10; % frames for acceleration (first frame will be 0 last at full speed, so practicall it is accFrames-2)
speed = [linspace(0,1,accFrames) ones(1,nFrames+1 -2*accFrames) linspace(1,0,accFrames)];
speed = speed(1:end-1); % last speed is 0, this does nothing in cumsum; (compensated by +1 frames in center)
angles = cumsum(speed)/sum(speed) *4*pi;
xLimits = [-13.2 13.2]; % ADJUST
yLimits = [-11.6 8.6]; % ADJUST
elseif versionNr == 2
curVers = 'positive_and_negative';
nFrames = 155;
accFrames = 10; % frames for acceleration (first frame will be 0 last at full speed, so practicall it is accFrames-2)
speed = [linspace(0,1,accFrames) ones(1,nFrames+1 -2*accFrames) linspace(1,0,accFrames)];
speed = speed(1:end-1); % last speed is 0, this does nothing in cumsum; (compensated by +1 frames in center)
angles = cumsum(speed)/sum(speed) *2*pi;
xLimits = [-13.2 13.2]; % ADJUST
yLimits = [-10.1 10.1]; % ADJUST
elseif versionNr == 3
curVers = 'in_and_out_tracing';
nFrames = 355;
accFrames = 10; % frames for acceleration (first frame will be 0 last at full speed, so practicall it is accFrames-2)
speed = [linspace(0,1,accFrames) ones(1,nFrames+1 -2*accFrames) linspace(1,0,accFrames)];
speed = speed(1:end-1); % last speed is 0, this does nothing in cumsum; (compensated by +1 frames in center)
angles = cumsum(speed)/sum(speed) *4*pi;
xLimits = [-13.2 13.2]; % ADJUST
yLimits = [-10.1 10.1]; % ADJUST
end
xRange = xLimits(2)-xLimits(1);
yRange = yLimits(2)-yLimits(1);
screenSize = get(groot,'Screensize')-[0 0 5 20]; % [1 1 width height] (minus tolerance for figure borders)
screenAspectRatio = screenSize(3)/screenSize(4); % width/height
imageAspectRatio = xRange/yRange;
MegaPixelTarget = 51*10^6; % Category:Animated GIF files exceeding the 50 MP limit
pxPerImage = MegaPixelTarget/nFrames; % pixel per gif frame
ySize = sqrt(pxPerImage/imageAspectRatio); % gif height
xSize = ySize*imageAspectRatio; % gif width
xSize = floor(xSize); ySize = floor(ySize); % full pixels
if imageAspectRatio > screenAspectRatio % width will be the problem
scaleReduction = floor(screenSize(3)/xSize); % repeat as often as possible
else % height will be the problem
scaleReduction = floor(screenSize(4)/ySize); % repeat as often as possible
end
figHandle = figure(25554461); clf
set(figHandle,'Units','pixel');
set(figHandle,'Position',[1 1 xSize*scaleReduction ySize*scaleReduction]); % big start image for antialiasing later [x y width height]
set(figHandle,'MenuBar','none', 'ToolBar','none'); % free real estate for a maximally large image
set(figHandle,'Color',RGB.bkgd); % white background
axesHandle = axes;
hold(axesHandle,'on')
axis off % invisible axes (no ticks)
axis equal;
setXYlim(axesHandle,xLimits,yLimits); % set limits and drawnow;
liSc = ySize*scaleReduction/800; % LineWidth scale; LineWidth is absolut, a bigger images needs thicker lines to keep them in proportion
reducedRGBimage = uint8(ones(ySize,xSize,3,nFrames)); % allocate
for iFrame = 1:nFrames
cla(axesHandle)
if versionNr == 1 % 'positive_tracing'
% a moving dotted line jitters, and looks bad; so it is drawn static an the unused part is covered up
plot([0 xLimits(2)+5],[0 0],':','Color',RGB.blue,'LineWidth', 6*liSc) % horizontal base line
plot([angles(iFrame) xLimits(2)+5],[0 0],'-','Color',RGB.bkgd,'LineWidth',10*liSc) % cover up unseen part
elseif versionNr == 2 % 'positive_and_negative'
plot(xLimits+[-5 5],[0 0],':','Color',RGB.blue,'LineWidth',6*liSc) % horizontal base line
elseif versionNr == 3 % 'in_and_out_tracing'
% a moving dotted line jitters, and looks bad; so it is drawn static an the unused part is covered up
plot([ 0 xLimits(2)+5],[0 0],':','Color',RGB.blue, 'LineWidth', 6*liSc) % horizontal base line
plot([ 0 xLimits(1)-5],[0 0],':','Color',RGB.violet,'LineWidth', 6*liSc) % horizontal base line
plot([ angles(iFrame) xLimits(2)+5],[0 0],'-','Color',RGB.bkgd, 'LineWidth',10*liSc) % cover up unseen part
plot([-angles(iFrame) xLimits(1)-5],[0 0],'-','Color',RGB.bkgd, 'LineWidth',10*liSc) % cover up unseen part
end
drawSpurWheel([0 0],teeth,module,RGB.brightGrey,2*liSc,RGB.black,-angles(iFrame) ); % cogwheel
sideOffset = angles(iFrame)*teeth*module/2;
drawRack([0 teeth*module/2],150,module,RGB.grey,2*liSc,RGB.black,sideOffset+ pi/16,1);
if versionNr == 3
drawRack([0 -teeth*module/2],150,module,RGB.grey,2*liSc,RGB.black,-sideOffset+ pi/16,0);
end
for iRotMark = (-4:4)*teeth*module*pi
plot([1 1]* (sideOffset+iRotMark), [10 17]*module,'-','Color',RGB.darkGrey,'LineWidth',4*liSc) % vertical marker on upper rack
if versionNr ==3
plot([1 1]* (-sideOffset+iRotMark), [10 17]*-module,'-','Color',RGB.darkGrey,'LineWidth',4*liSc) % vertical marker on lower rack
end
end
xCoord = [4 0 0];
yCoord = [0 0 4];
rotAngle = -angles(iFrame);
if iFrame == nFrames
rotAngle = 0; % fix slightly angled lines
end
[xCoord,yCoord] = rotateCordiantes(xCoord,yCoord,rotAngle);
plot(xCoord,yCoord,'-','Color','k','LineWidth',4*liSc) % coordinate system lines
xArrow = [4.5 4.0 4.0];
yArrow = [0 -0.15 0.15];
[xArrow,yArrow] = rotateCordiantes(xArrow,yArrow,rotAngle);
patch(xArrow,yArrow,'k');
[xArrow,yArrow] = rotateCordiantes(xArrow,yArrow,pi/2);
patch(xArrow,yArrow,'k');
curvePoints = linspace(0,8*pi,500);
[x,y] = pol2cart(curvePoints-angles(iFrame),curvePoints);
if versionNr == 1 % 'positive_tracing'
plot(x,y, '-','Color',RGB.red ,'LineWidth',3*liSc) % curve
[x,y] = pol2cart(angles(1:iFrame)-angles(iFrame),angles(1:iFrame));
plot( x,y, '-','Color',RGB.red ,'LineWidth',7*liSc) % trace curve
plot(sideOffset*[1 1],[0 8*module],'-','Color',RGB.blue,'LineWidth',6*liSc) % verical base line
plot(sideOffset,0,'.','Color',RGB.red, 'MarkerSize',60*liSc,'LineWidth',5*liSc) % color marker on trace point of curve
plot(sideOffset,0,'o','Color',RGB.blue ,'MarkerSize',20*liSc,'LineWidth',5*liSc) % color marker on trace point of curve
elseif versionNr == 2 % 'positive_and_negative'
[xa,ya] = pol2cart(-curvePoints-angles(iFrame),-curvePoints);
plot(xa,ya, '-','Color',RGB.cyan ,'LineWidth',7*liSc) % anti-curve
plot( x, y, '-','Color',RGB.red ,'LineWidth',7*liSc) % curve
for iRotMark = (-4:4)*teeth*module*pi
plot(sideOffset*[1 1]+iRotMark,[0 8*module],'-','Color',RGB.blue,'LineWidth',6*liSc) % verical base line
end
for iRotMark = (-4:4)*teeth*module*pi
if sideOffset+iRotMark >= 0
plot(sideOffset+iRotMark,0,'.','Color',RGB.red ,'MarkerSize',60*liSc,'LineWidth',5*liSc) % color marker on trace point of curve
else
plot(sideOffset+iRotMark,0,'.','Color',RGB.cyan ,'MarkerSize',60*liSc,'LineWidth',5*liSc) % color marker on trace point of curve
end
plot(sideOffset+iRotMark,0,'o','Color',RGB.blue ,'MarkerSize',20*liSc,'LineWidth',5*liSc) % color marker on trace point of curve
end
if iFrame == nFrames
plot(0,0,'.','Color',RGB.cyan ,'MarkerSize',60*liSc,'LineWidth',5*liSc) % color marker on trace point of curve
plot(0,0,'o','Color',RGB.blue ,'MarkerSize',20*liSc,'LineWidth',5*liSc) % color marker on trace point of curve
end
elseif versionNr == 3 % 'in_and_out_tracing'
plot(-x,-y,'-','Color',RGB.green,'LineWidth',3*liSc) % anti curve
plot( x, y,'-','Color',RGB.red, 'LineWidth',3*liSc) % curve
[x,y] = pol2cart(angles(1:iFrame)-angles(iFrame),angles(1:iFrame));
plot(-x,-y,'-','Color',RGB.green ,'LineWidth',7*liSc) % trace anti curve
plot( x, y,'-','Color',RGB.red, 'LineWidth',7*liSc) % trace curve
plot( sideOffset*[1 1], [0 8*module],'-','Color',RGB.blue, 'LineWidth',6*liSc) % verical base line
plot(-sideOffset*[1 1],-[0 8*module],'-','Color',RGB.violet,'LineWidth',6*liSc) % verical base line
plot(-sideOffset,0,'.','Color',RGB.green, 'MarkerSize',60*liSc,'LineWidth',5*liSc) % color marker on trace point of curve
plot(-sideOffset,0,'o','Color',RGB.violet ,'MarkerSize',20*liSc,'LineWidth',5*liSc) % color marker on trace point of curve
plot(sideOffset,0,'.','Color',RGB.red, 'MarkerSize',60*liSc,'LineWidth',5*liSc) % color marker on trace point of curve
plot(sideOffset,0,'o','Color',RGB.blue ,'MarkerSize',20*liSc,'LineWidth',5*liSc) % color marker on trace point of curve
end
%% save animation
setXYlim(axesHandle,xLimits,yLimits); % reset limits and drawnow
f = getframe(figHandle);
reducedRGBimage(:,:,:,iFrame) = imReduceSize(f.cdata,scaleReduction); % the size reduction: adds antialiasing
if iFrame == nFrames % SVG
if ~isempty(which('plot2svg'))
plot2svg(fullfile(pathstr, [fname '_' curVers '.svg']),figHandle) % by Juerg Schwizer
else
disp('plot2svg.m not available; see http://www.zhinst.com/blogs/schwizer/');
end
end
end
RGBcurrent = RGB; % copy colormap; to be pruned to the used colors
if versionNr == 1
RGBcurrent = rmfield(RGBcurrent,{'green','violet','cyan'}); % remove unused colors
nColors = 32;
elseif versionNr == 2
RGBcurrent = rmfield(RGBcurrent,{'green','violet'}); % remove unused colors
nColors = 64;
elseif versionNr == 3
RGBcurrent = rmfield(RGBcurrent,{'cyan'}); % remove unused colors
nColors = 64;
end
startMap = cell2mat(struct2cell(RGBcurrent)); % struct2colormap; % list of map colors that are not allowed to be changed
map = createImMap(reducedRGBimage,nColors,startMap); % full colormap
im = uint8(ones(ySize,xSize,1,nFrames)); % allocate
for iFrame = 1:nFrames
im(:,:,1,iFrame) = rgb2ind(reducedRGBimage(:,:,:,iFrame),map,'nodither');
end
imwrite(im,map,fullfile(pathstr, [fname '_' curVers '.gif']),'DelayTime',1/25,'LoopCount',inf) % save gif
disp([fname '_' curVers '.gif has ' num2str(numel(im)/10^6 ,4) ' Megapixels']) % Category:Animated GIF files exceeding the 50 MP limit
end
function drawSpurWheel(center,toothNumber,module,fillC,linW,linC,startOffset)
% DRAWSPURWHEEL - draw a simple Toothed Wheel
% center: [x y]
% toothNumber: scalar
% module: scalar tooth "size"
% fillC: color of filling [r g b]
% linW: LineWidth
% linC: LineColor
% startOffset: start rotation (scalar)[rad]
effectiveRadius = module*toothNumber/2; % effective Radius
outsideRadius = effectiveRadius+1* module; % +---+ +---+
upperRisingRadius = effectiveRadius+0.5*module; % / \ / \
% effective Radius % / \ / \
lowerRisingRadius = effectiveRadius-0.5*module; % I I I I
rootRadius = effectiveRadius-1.1*module; % + - - - + + - - - + +
angleBetweenTeeth = 2*pi/toothNumber; % angle between 2 teeth
angleOffPoints = (0:angleBetweenTeeth/16:(2*pi));
angleOffPoints = angleOffPoints+startOffset; % apply rotation offset
angleOffPoints(7:16:end) = angleOffPoints(7:16:end) + 1/toothNumber^1.2; % hack to create smaller tooth tip
angleOffPoints(11:16:end) = angleOffPoints(11:16:end) - 1/toothNumber^1.2; % hack to create smaller tooth tip
angleOffPoints(8:16:end) = (angleOffPoints(7:16:end) + angleOffPoints(9:16:end))/2; % shift the neighbouring tip point in accordingly
angleOffPoints(10:16:end) = (angleOffPoints(11:16:end) + angleOffPoints(9:16:end))/2; % shift the neighbouring tip point in accordingly
angleOffPoints(6:16:end) = angleOffPoints(6:16:end) + 1/toothNumber^1.7; % hack to create slender upperRisingRadius
angleOffPoints(12:16:end) = angleOffPoints(12:16:end) - 1/toothNumber^1.7; % hack to create slender upperRisingRadius
radiusOffPoints = angleOffPoints; % allocate with correct site
radiusOffPoints( 1:16:end) = rootRadius; % center bottom I
radiusOffPoints( 2:16:end) = rootRadius; % left bottom I
radiusOffPoints( 3:16:end) = rootRadius; % left bottom corner +
radiusOffPoints( 4:16:end) = lowerRisingRadius; % lower rising bottom \
radiusOffPoints( 5:16:end) = effectiveRadius; % rising edge \
radiusOffPoints( 6:16:end) = upperRisingRadius; % upper rising edge \
radiusOffPoints( 7:16:end) = outsideRadius; % right top corner +
radiusOffPoints( 8:16:end) = outsideRadius; % right top I
radiusOffPoints( 9:16:end) = outsideRadius; % center top I
radiusOffPoints(10:16:end) = outsideRadius; % left top I
radiusOffPoints(11:16:end) = outsideRadius; % left top corner +
radiusOffPoints(12:16:end) = upperRisingRadius; % upper falling edge /
radiusOffPoints(13:16:end) = effectiveRadius; % falling edge /
radiusOffPoints(14:16:end) = lowerRisingRadius; % lower falling edge /
radiusOffPoints(15:16:end) = rootRadius; % right bottom corner +
radiusOffPoints(16:16:end) = rootRadius; % right bottom I
[X,Y] = pol2cart(angleOffPoints,radiusOffPoints);
X = X+center(1); % center offset
Y = Y+center(2); % center offset
patch(X,Y,fillC,'EdgeColor',linC,'LineWidth',linW)
function drawRack(center,toothNumber,module,fillC,linW,linC,startOffset,top)
% center: [x y]
% toothNumber: scalar
% module: scalar tooth "size"
% fillC: color of filling [r g b]
% linW: LineWidth
% linC: LineColor
% startOffset: initial shift
% top: 1=top 0=bottom
x = (0:toothNumber*4-1)*pi*module/4;
x = x-mean(x)+center(1)+startOffset;
y = zeros(size(x));
y(1:4:end) = y(1:4:end)+1.1*module; % +###I bottom
y(2:4:end) = y(2:4:end)-1 *module; % +######I tip
y(3:4:end) = y(3:4:end)-1 *module; % +######I tip
y(4:4:end) = y(4:4:end)+1.1*module; % +###I bottom
x(1:4:end) = x(1:4:end)-0.14*module; % bottom smaller
x(2:4:end) = x(2:4:end)+0.14*module; % tip smaller
x(3:4:end) = x(3:4:end)-0.14*module; % tip smaller
x(4:4:end) = x(4:4:end)+0.14*module; % bottom smaller
x = [x(1) x x(end)];
y = [y(1)+9*module y y(end)+9*module];
if ~top
y = -y; % flip
end
y = y+center(2);
patch(x,y,fillC,'EdgeColor',linC,'LineWidth',linW);
function setXYlim(axesHandle,xLimits,yLimits)
% set limits; practically the axis overhangs the figure all around, to
% hide rendering error at line-ends.
% Input:
% axesHandle:
% xLimits, yLimits: [min max]
overh = 0.05; % 5% overhang all around; 10% bigger in x and y
xlim([+xLimits(1)*(1+overh)-xLimits(2)*overh -xLimits(1)*overh+xLimits(2)*(1+overh)])
ylim([+yLimits(1)*(1+overh)-yLimits(2)*overh -yLimits(1)*overh+yLimits(2)*(1+overh)])
set(axesHandle,'Position',[-overh -overh 1+2*overh 1+2*overh]); % stretch axis as bigger as figure, [x y width height]
drawnow;
function [x,y] = rotateCordiantes(x,y,anglee)
% x coordinates of the center
% y coordinates of the center
% anglee angle of rotation in [rad]
rotM = [cos(anglee) -sin(anglee); sin(anglee) cos(anglee)];
x_y = rotM*[x(:)';y(:)'];
x = x_y(1,:);
y = x_y(2,:);
function im = imReduceSize(im,redSize)
% Input:
% im: image, [imRows x imColumns x nChannel x nStack] (unit8)
% imRows, imColumns: must be divisible by redSize
% nChannel: usually 3 (RGB) or 1 (grey)
% nStack: number of stacked images
% usually 1; >1 for animations
% redSize: 2 = half the size (quarter of pixels)
% 3 = third the size (ninth of pixels)
% ... and so on
% Output:
% im: [imRows/redSize x imColumns/redSize x nChannel x nStack] (unit8)
%
% an alternative is: imNew = imresize(im,1/reduceImage,'bilinear');
% BUT 'bicubic' & 'bilinear' produces fuzzy lines
% IMHO this function produces nicer results as "imresize"
[nRow,nCol,nChannel,nStack] = size(im);
if redSize==1; return; end % nothing to do
if redSize~=round(abs(redSize)); error('"redSize" must be a positive integer'); end
if rem(nRow,redSize)~=0; error('number of pixel-rows must be a multiple of "redSize"'); end
if rem(nCol,redSize)~=0; error('number of pixel-columns must be a multiple of "redSize"'); end
nRowNew = nRow/redSize;
nColNew = nCol/redSize;
im = double(im).^2; % brightness rescaling from "linear to the human eye" to the "physics domain"; see youtube: /watch?v=LKnqECcg6Gw
im = reshape(im, nRow, redSize, nColNew*nChannel*nStack); % packets of width redSize, as columns next to each other
im = sum(im,2); % sum in all rows. Size of result: [nRow, 1, nColNew*nChannel]
im = permute(im, [3,1,2,4]); % move singleton-dimension-2 to dimension-3; transpose image. Size of result: [nColNew*nChannel, nRow, 1]
im = reshape(im, nColNew*nChannel*nStack, redSize, nRowNew); % packets of width redSize, as columns next to each other
im = sum(im,2); % sum in all rows. Size of result: [nColNew*nChannel, 1, nRowNew]
im = permute(im, [3,1,2,4]); % move singleton-dimension-2 to dimension-3; transpose image back. Size of result: [nRowNew, nColNew*nChannel, 1]
im = reshape(im, nRowNew, nColNew, nChannel, nStack); % putting all channels (rgb) back behind each other in the third dimension
im = uint8(sqrt(im./redSize^2)); % mean; re-normalize brightness: "scale linear to the human eye"; back in uint8
function map = createImMap(imRGB,nCol,startMap)
% createImMap creates a color-map including predefined colors.
% "rgb2ind" creates a map but there is no option to predefine some colors,
% and it does not handle stacked images.
% Input:
% imRGB: image, [imRows x imColumns x 3(RGB) x nStack] (unit8)
% nCol: total number of colors the map should have, [integer]
% startMap: predefined colors; colormap format, [p x 3] (double)
imRGB = permute(imRGB,[1 2 4 3]); % step1; make unified column-image (handling possible nStack)
imRGBcolumn = reshape(imRGB,[],1,3,1); % step2; make unified column-image
fullMap = double(permute(imRGBcolumn,[1 3 2]))./255; % "column image" to color map
[fullMap,~,imMapColumn] = unique(fullMap,'rows'); % find all unique colors; create indexed colormap-image
% "cmunique" could be used but is buggy and inconvenient because the output changes between "uint8" and "double"
nColFul = size(fullMap,1);
nColStart = size(startMap,1);
disp(['Number of colors: ' num2str(nColFul) ' (including ' num2str(nColStart) ' self defined)']);
if nCol<=nColStart; error('Not enough colors'); end
if nCol>nColFul; warning('More colors than needed'); end
isPreDefCol = false(size(imMapColumn)); % init
for iCol = 1:nColStart
diff = sum(abs(fullMap-repmat(startMap(iCol,:),nColFul,1)),2); % difference between a predefined and all colors
[mDiff,index] = min(diff); % find matching (or most similar) color
if mDiff>0.05 % color handling is not precise
warning(['Predefined color ' num2str(iCol) ' does not appear in image'])
continue
end
isThisPreDefCol = imMapColumn==index; % find all pixel with predefined color
disp([num2str(sum(isThisPreDefCol(:))) ' pixel have predefined color ' num2str(iCol)]);
isPreDefCol = or(isPreDefCol,isThisPreDefCol); % combine with overall list
end
[~,mapAdditional] = rgb2ind(imRGBcolumn(~isPreDefCol,:,:),nCol-nColStart,'nodither'); % create map of remaining colors
map = [startMap;mapAdditional];
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Licensing[edit]
I, the copyright holder of this work, hereby publish it under the following license:
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. | |
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 00:21, 17 February 2019 | 433 × 331 (4.26 MB) | Jahobr (talk | contribs) | better colormap | |
13:07, 24 June 2017 | 430 × 330 (4.14 MB) | Jahobr (talk | contribs) | User created page with UploadWizard |
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